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IL-SANG AHN, Ph.D. Research Scientist

Assessment of Lead-Rubber Bearings in Bridges: Application of Nonlinear Model Based System Identification. IL-SANG AHN, Ph.D. Research Scientist Department of Civil, Structural and Environmental Engineering University at Buffalo. Column Damages from Earthquakes. San Fernando (2/9/1971) M6.6.

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IL-SANG AHN, Ph.D. Research Scientist

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  1. Assessment of Lead-Rubber Bearings in Bridges: Application of Nonlinear Model Based System Identification IL-SANG AHN, Ph.D.Research Scientist Department of Civil, Structural and Environmental Engineering University at Buffalo

  2. Column Damages from Earthquakes San Fernando (2/9/1971) M6.6

  3. Column Damages from Earthquakes Loma Prieta (10/17/1989) M7.1

  4. Column Damages from Earthquakes Northridge (1/17/1994) M6.7

  5. Background • Earthquake Protection • Seismic Isolation is an effective way to protect new and old bridges • Lead-Rubber Bearings are the most widely used Base Isolators • Aging and Temperature dependency of Lead-Rubber Bearings ? • Field Experiments on Lead-Rubber Bearings • A three span continuous steel girder bridge in Western NY was seismically rehabilitated with lead-rubber bearings • Field experiments were conducted from 1994 to 1999 • Seismic performance between conventional steel bearings and seismic bearings • A rare case to assess effects due to aging and temperature variations by FIELD EXPERIMENTS!

  6. Basic Principles of Seismic Isolation Basic Idea: Uncoupling a bridge superstructure from the horizontal components of earthquake ground motion Conventional Base Isolated • Requirements of Base Isolator: • flexibility to lengthen the period of vibration of the bridge • energy dissipation • adequate rigidity for service loads Period Shift Damping

  7. Population of Base Isolated Bridges States with More Than Ten Isolated Bridges (2003) Note: Isolated bridges in U.S., Canada, Mexico, and Puerto Rico ¾ of the isolated bridges in the U.S. use Lead Rubber Bearings

  8. Location of the Subject Bridge Rte 400, Western New York State

  9. Plan and Elevation of the Subject Bridge Girder 7 - W36x150 Steel Beam Deck 230mm thick Conc. Abutments Lead Rubber Bearings Piers Elastomeric Bearings

  10. Lead Rubber Bearing • Shapes and Size • Square Shape (279mm  279mm) • 10 Rubber layers (Natural Rubber satisfying ASTM D4014) • Lead Core Diameter : 64mm

  11. Field Experiment: Pull-Back Testing Basic Idea: a free vibration test method where lateral forces are applied to the superstructure and released quickly to introduce a free vibration developed and applied from the 1970s Application to base isolated bridges • Mangatewai-Iti bridge in New Zealand : Lam 1990 • Four-span base isolated viaduct in Walnut Creek in California : Gilani et al. 1995 • Three-span continuous PC I-girder bridge over Minor Slough in Kentucky: Robson and Harik 1998 • Three-span continuous steel-girder bridge over Cazenovia Creek : Wendichansky et al. 1998, Hu 1998

  12. Pull-Back Testing Two-Pier Test vs. One-Pier Test • One-Pier Test Two-Pier Test

  13. Pull-Back Testing on the Subject Bridge Test Setting

  14. Instrumentation Accelerometer Location (Part)

  15. Pull-Back Test Summary History

  16. Bridge Deck Motion Rigid Body Motion of the Superstructure

  17. Test Results Measured Acceleration and Displacement QR94-3 QR98-1 QR99-1

  18. System Identification Definition: determination of a system to which the system under test is equivalent (Åström and Eykhoff 1971) Nonlinearity is one of the unique features and difficulties in the application of system identification to civil structures (Imai et al. 1991) : • Nonlinear Model-Based Approach • Two DOF dynamic governing equation: Transverse displacement + Rotation • Lead Rubber Bearing: Menegotto-Pinto Model • QR94-3 vs. QR98-1, QR98-1 vs. QR99-1 • Issues of the subject problem • Nonlinearity • Variations among experiments • Uncertainties from expansion joint properties

  19. Governing TDOF Eqn. of Bridge Deck Motion Rigid Body Motion of the Superstructure where Menegotto-Pinto Model

  20. System Identification Procedures • 1st Phase: Superstructure Overall Behavior • Transverse displacement and Rotation at the Center of Mass • Abutment:  seven LRB + Expansion Joint • Pier:  seven elastomeric bearings + Pier Stiffness 2nd Phase: Lead Rubber Bearing

  21. System Identification (1st Phase) System Identification  Optimization Problem: For given models and input, the output is function of parameters in the governing equation. System identification becomes an optimization problem to seek optimal values of the parameters to minimize the difference between measured and reproduced responses. Optimization Formulation

  22. System Identification Results (1st Phase)

  23. System Identification (1st Phase) QR94-3 vs. QR98-1

  24. System Identification Procedures 1st Phase: Superstructure Overall Behavior • 2nd Phase: Lead Rubber Bearing • Force-Displacement at the south abutment from the 1st phase • LRB and the Expansion Joint are separated • Uncertainty of the Expansion JointMeasured expansion joint stiffness:5,250 kN/m (laboratory test) Random Variable

  25. System Identification (2nd Phase) Optimization Formulation for expansion joint Notes force from the first phase of SI

  26. System Identification (2nd Phase) QR94-3 vs. QR98-1 (10% uncertainty range)

  27. System Identification (2nd Phase) QR98-1 vs. QR99-1 (10% uncertainty range)

  28. System Identification (2nd Phase) • Randomly Selected Initial Stiffness of Expansion Joint • Repeat Optimization for Each Test e.g. Test A and Test B • Results: Sets of Parameters for Each Test • Comparison between Two Tests • Compare Parameters: mislead the decision on their closeness • Compare Force Responses under Test Disps.Random Variables (Normal Distribution) • Treating Force Random Variables • Take Differences : Normal Distribution • Ensemble Average: Standard Normal Distribution • Sum of Ensemble Average: Chi-Square Distribution

  29. Hypothesis Testing • Hypothesis Testing • null hypothesis: “forces from two models are the same” • calculate random variables and compare with chi-square distribution • if the hypothesis is rejected : two models are different • if it is accepted: two models are statistically indistinguishable Hypothesis Testing Results

  30. Identified Behavior of Lead Rubber Bearing Force Time History Force-Displacement Aging Effects (QR94-3 vs. QR98-1) Temperature Effects (QR98-1 vs. QR99-1)

  31. Quantitative Comparison

  32. Results Comparison • Stiffness increases due to Aging • increased modulus of rubber • Natural aging of rubber-changes in physical properties over 40 years by Brown and Butler - the strength and elongation at break of rubber reduced drastically - special attention is warranted before utilizing stiffening effects Stiffness increases due to temperature drop: Consistent with Lab. experiment • Energy dissipation capacity reduction due to temperature dropping: • Contradictory to the Lab. Experiment • low strain in pull-back tests • full-cycle vs. free vibration Laboratory Test Results

  33. Summary and Conclusions • A nonlinear model-based system identification method is developed and applied to the investigation of aging and temperature effects of lead-rubber bearings based on three pull-back tests of a three-span continuous bridge. • The two degree-of-freedom governing equations for transverse and rotational rigid-body motion of the superstructure can successfully capture free-vibration motion in pull-back tests. • The Menegotto-Pinto model suitably represents hysteretic damping behavior of bearings under the free-vibration condition. • In order to investigate aging and temperature dependent effects of bearings, hypothesis testing is applied to the chi-square distribution of restoring forces. • Regarding aging effects, increases of the pre-yielding stiffness and the post-yielding stiffness are observed. • Regarding temperature dropping effects, the decrease of energy dissipation capacity and the increase of the pre-yielding stiffness are observed.

  34. Thank You ! Questions & Comments

  35. Damages on Bridges from Earthquakes San Francisco Earthquake (4/18/1906) M7.7 Bridge in Alexander Valley

  36. Damages on Bridges from Earthquakes San Fernando (2/9/1971) M6.6 Interchange on Interstate Highways 5 and 210

  37. Damages on Bridges from Earthquakes Loma Prieta (10/17/1989) M7.1 Oakland Bay Bridge

  38. Damages on Bridges from Earthquakes Northridge (1/17/1994) M6.7 Interchange on Interstate Highways 5 and 14

  39. Damages on Bridges from Earthquakes San Fernando (2/9/1971) M6.6

  40. LRB Installation Works Installation Process

  41. Rehabilitation History Purposes of the Rehabilitation • Seismic Retrofit • Concrete Deck Replacement Procedures of the Seismic Retrofit • Laboratory bearing test • Bearing replacement • In-Situ bridge tests: Pull-back test

  42. Pull-Back Testing Over Deck Test vs. Under Deck Test Over Deck Test Under Deck Test

  43. Instrumentation Accelerometers and Potentiometers at Piers and Abutments Accelerometers Potentiometers

  44. Hysteretic Damping Model of LRB Menegotto-Pinto Model Restoring force Displacement Force and Disp. at direction changing point Post-yielding stiffness / Pre-yielding stiff Force and Disp. at the yield point for initial loading for unloading and reloading

  45. Nondimensional Combined Governing EQ. Nondimensional Variables Transverse displacement : where Max. measured disp. Force at uo Radius of gyration Rotational displacement : Time : Nondimensional Combined Governing Equations where

  46. System Identification Post-Processing QR98-1 vs. QR99-1

  47. System Identification (2nd Phase) • Test Displacement Functions • Seven (j=1-7) displacement function • Max Amplitude 5 mm – 35 mm • Period : 0.5 sec (i=26 data points) Forces at data point i under test displacement j For Test A For Test B

  48. System Identification (2nd Phase) Forces at data point i under test displacement j For Test A For Test B

  49. System Identification (2nd Phase) • Probability Distribution (comparison between Test A and Test B) • the random variable has • if two means are the same and the s.t.d is a constant, then the standard normal distribution becomes

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